Method and system for fast calibration of three-dimensional (3D) sensors

ABSTRACT

Rapid calibration of a TOF system uses a stationary target object and electrically introduces phase shift into the TOF system to emulate target object relocation. Relatively few parameters suffice to model a parameterized mathematical representation of the transfer function between measured phase and Z distance. The phase-vs-distance model is directly evaluated during actual run-time operation of the TOF system. Preferably modeling includes two components: electrical modeling of phase-vs-distance characteristics that depend upon electrical rather than geometric characteristics of the sensing system, and elliptical modeling that phase-vs-distance characteristics that depending upon geometric rather than electrical characteristics of the sensing system.

RELATION TO PENDING APPLICATION

Priority is claimed to U.S. patent application Ser. No. 11/825,582 filed6 Jul. 2007 entitled “Method and System for Fast Calibration ofThree-Dimensional (3D) Sensors”, soon to issue as U.S. Pat. No.7,471,376, which application claimed priority to provisional patentapplication Ser. No. 60/818,819 filed 6 Jul. 2006, entitled Method andSystem for Fast Calibration of Three-Dimensional (3D) Sensors.

BACKGROUND OF THE INVENTION

Three-dimensional (3D) cameras (or sensors) based on time-of-flight(TOF) principle acquire distance information from object(s) in a scenebeing imaged. Distance information is produced independently at eachpixel of the camera's sensor. Exemplary such systems are described inU.S. Pat. No. 6,323,942 “CMOS-Compatible Three-Dimensional Image SensorIC” (2001), and U.S. Pat. No. 6,515,740 “Methods for CMOS-CompatibleThree-Dimensional Image Sensing Using Quantum Efficiency Modulation”2003, which patents are assigned to Canesta, Inc., presently ofSunnyvale, Calif.

As described in U.S. Pat. No. 6,323,942, a TOF system emits opticalenergy and determines how long it takes until at least some of thatenergy reflected by a target object arrives back at the system to bedetected. Emitted optical energy traversing to more distant surfaceregions of a target object before being reflected back toward the systemwill define a longer TOF than if the target object were closer to thesystem. If the roundtrip TOF time is denoted t1, then the distancebetween target object and the TOF system is Z1, where Z1=t1·C/2, where Cis velocity of light. Such systems can acquire both luminosity date(signal amplitude) and TOF distance, and can realize three-dimensionalimages of a target object in real time.

A more sophisticated TOF system is described in U.S. Pat. No. 6,515,740,wherein TOF is determined by examining relative phase shift betweentransmitted light signals and light signals reflected from a targetobject. FIG. 1A depicts an exemplary phase-shift detection system 100according to the '740 patent. Detection of the reflected light signalsover multiple locations in the system pixel array results in measurementsignals that are referred to as depth images. The depth images representa three-dimensional image of the target object surface.

Referring to FIG. 1A, TOF system 100 includes a two-dimensional array130 of pixel detectors 140, each of which has dedicated circuitry 150for processing detection charge output by the associated detector. In atypical application, array 130 might include 100×100 pixels 230, andthus include 100×100 processing circuits 150. IC 110 may also include amicroprocessor or microcontroller unit 160, memory 170 (which preferablyincludes random access memory or RAM and read-only memory or ROM), ahigh speed distributable clock 180, and various computing andinput/output (I/O) circuitry 190. Among other functions, controller unit160 may perform distance to object and object velocity calculations.

Under control of microprocessor 160, a source of optical energy 120 isperiodically energized via exciter 115, and emits optical energy vialens 125 toward an object target 20. Typically the optical energy islight, for example emitted by a laser diode, VCSEL (vertical-cavitysurface emitting laser) or LED device 120. Some of the optical energyemitted from device 120 will be reflected off the surface of targetobject 20, and will pass through an aperture field stop and lens,collectively 135, and will fall upon two-dimensional array 130 of pixeldetectors 140 where an image is formed. In some implementations, eachimaging pixel detector 140 captures time-of-flight (TOF) required foroptical energy transmitted by emitter 120 to reach target object 20 andbe reflected back for detection by two-dimensional sensor array 130.Using this TOF information, distances Z can be determined.Advantageously system 100 can be implemented on a single IC 110, withoutmoving parts and with relatively few off-chip components.

Typically optical energy source 20 emits preferably low power (e.g.,perhaps 1 W peak) periodic waveforms, producing optical energy emissionsof known frequency (perhaps 30 MHz to a many hundred MHz) for a timeperiod known as the shutter time (perhaps 10 ms). Optical energy fromemitter 120 and detected optical energy signals within pixel detectors140 are synchronous to each other such that phase difference and thusdistance Z can be measured for each pixel detector. The detection methodused is referred to as homodyne detection in the '740 and '496 patents.Phase-based homodyne detection TOF systems are also described in U.S.Pat. No. 6,906,793, Methods and Devices for Charge Management forThree-Dimensional Sensing, assigned to Canesta, Inc., assignee herein.

The optical energy detected by the two-dimensional imaging sensor array130 will include light source amplitude or intensity information,denoted as “A”, as well as phase shift information, denoted as φ. Asdepicted in exemplary waveforms in FIGS. 1B and 1C, the received phaseshift information (FIG. 1C) varies with TOF and can be processed toyield Z data. For each pulse train of optical energy transmitted byemitter 120, a three-dimensional image of the visible portion of targetobject 20 is acquired, from which intensity and Z data is obtained(DATA). As described in U.S. Pat. Nos. 6,515,740 and 6,580,496 obtainingdepth information Z requires acquiring at least two samples of thetarget object (or scene) 20 with 90° phase shift between emitted opticalenergy and the pixel detected signals. While two samples is a minimumfigure, preferably four samples, 90° apart in phase, are acquired topermit detection error reduction due to mismatches in pixel detectorperformance, mismatches in associated electronic implementations, andother errors. On a per pixel detector basis, the measured four sampledata are combined to produce actual Z depth information data. Furtherdetails as to implementation of various embodiments of phase shiftsystems may be found in U.S. Pat. Nos. 6,515,740 and 6,580,496.

FIG. 1D is similar to what is described with respect to the fixed phasedelay embodiment of FIG. 10 in U.S. Pat. No. 6,580,496, entitled Systemsfor CMOS-Compatible Three-Dimensional Image Sensing Using QuantumEfficiency Modulation, or in U.S. Pat. No. 7,906,793, entitled Methodsand Devices for Charge Management for Three-Dimensional Sensing, bothpatents assigned to Canesta, Inc., assignee herein. In FIG. 1D,generated photocurrent from each quantum efficiency modulateddifferential pixel detector, e.g., 140-1, is differentially detected(DIF. DETECT) and differentially amplified (AMP) to yield signalsB·cos(φ), B·sin(φ), where B is a brightness coefficient.

During normal run-time operation of the TOF system, a fixed 0° or 90°phase shift delay (DELAY) is switchably insertable responsive to a phaseselect control signal (PHASE SELECT). Homodyne mixing occurs usingquantum efficiency modulation to derive phase difference betweentransmitted and received signals (see FIGS. 1B, 1C), and to derive TOF,among other data. A more detailed description of homodyne detection inphase-based TOF systems is found in the '496 patent. Although sinusoidaltype periodic waveforms are indicated in FIG. 1D, non-sinusoidalwaveforms may instead be used. As described later herein, the detectioncircuitry of FIG. 1D may be used with embodiments of the presentinvention.

In many applications it is advantageous to have geometric information assuch information makes it easier to perceive and interact with the realworld. As noted, three-dimensional TOF camera systems includingexemplary system 100 in FIG. 1A accomplish this task using a modulatedlight source 120 (e.g., an LED, a laser, a VCSEL, etc.) to illuminate ascene containing a target object 20. The light reflected from the sceneis processed in the camera's sensor pixels to determine the phase delay(φ) between the transmitted light and reflected light. Phase delay (orsimply phase herein) is proportional to the (Z) distance between thesensor and the target. However phase delay is a relative quantity and isnot per se equal to Z distance. For example as Z increases, phase φincreases, but after an increase of 360°, the phase folds-over andfurther increases in Z will produce further increases in φ, againstarting from 0°. It is thus necessary to disambiguate or de-alias thephase data to obtain a true measure of Z.

Furthermore, the sensor's pixels measure phase delay along a certainradial angle that is different for each pixel 140 in array 130. Howevermany applications prefer using Cartesian (or real world X,Y,Z)coordinates instead of radial information. A mechanism is needed toestablish correspondence or mapping between phase and real worldcoordinates. Such a mechanism is obtained through a calibration process.

Thus, one function of calibration may be defined as creating a mappingfrom the sensor 140 response to geometrical coordinates, which are X, Y,and Z information with respect to a known reference. As used herein, Xand Y coordinates are the horizontal and vertical offsets from theoptical axis of the system, and Z is the perpendicular distance betweenthe sensor and the target object (e.g., object in a scene). Typicallythe calibration process includes several steps, where each step createsone kind of mapping. For instance, the mapping for real-world Zcoordinates is done by a step called Z (distance or depth) calibration,while the mapping for real-world X,Y coordinates is done by another stepcalled XY calibration.

In addition to geometrical calibration, one must perform other types ofcalibration to account for certain environmental factors, includingwithout limitation temperature and ambient lighting conditions. Forexample, temperature changes in sensor array 130 can increase so-calleddark current in pixels 140, which dark current can in turn changemeasured phase φ. Ambient light can interfere with system-emitted lightfrom source 120, and can result in phase errors. A complete calibrationprocedure preferably will include steps to model the effects of suchenvironmental changes. So doing can allow these effects to be removeddynamically during run-time operation, when the environmental conditionsmay change.

Consider for example distance (Z) calibration techniques, according tothe prior art. One known calibration method for a three-dimensionalsystem captures sensor phase response for a number of known Z distancevalues as the target object is successively moved or relocated in the XYplane. This prior art calibration method will be referred to herein asthe “by-example” method. Using this method sensor data from array 130are captured for each target object location and stored in memory. Theresultant phase-vs.-distance curve is constructed as a calibration tableof sensor response-distance pairs that is sampled at several values ofdistance. During actual run-time operation of the TOF system socalibrated, perhaps system 100, the stored calibration table data isinterpolated and bracketed to determine Z distance for a given sensorphase response. Thus, a given phase response from the sensor array isconverted to distance by interpolating the values stored in thecalibration table. However the phase-vs-distance transfer function curvecontains harmonics and sufficient data points must be stored in thecalibration table to model these harmonics to avoid loss of accuracy dueto insufficient sampling. There is also interpolation error that canonly be reduced by increasing the size of the table.

Although the “by-example” method is straightforward to implement withrelatively fast run-time processing, it has several disadvantages.Taking a subset of the operating range and subsequent interpolationresults in errors that can be several cm in magnitude. Further, as theoperating range of the sensor is increased, more data must be stored inthe calibration table to maintain accuracy. This generates largercalibration tables, requiring more storage, as well as longerinterpolation times. Storage can be on the order of several MB, e.g.,very large for use with embedded systems. Another problem from apractical standpoint is the large physical space needed to capture datafrom the sensor for large field of view (FOV) and operating ranges asthe target object is repositioned. For example, a sensor with a 100° FOVand 5 m operating range requires a target object of approximately 12m×12 m, which target object must be moved between 0 and 5 m duringcalibration. Given enough physical space for target object relocationduring calibration, and given enough time for the calibration procedure,such prior art “by example” calibration can be carried out. But suchprior art calibration procedure has high costs and is not very suitablefor calibrating a high-volume product.

What is needed are more efficient methods and systems to implementdetected phase to distance calibration for three-dimensional camerasystems. Such methods and systems should require less time and smallerphysical space to be carried out, and the calibration data shouldrequire less space for storage for use during system run-time operation.Preferably such calibration should provide a first model that dependsupon electrical rather than physical characteristics of the sensors inthe system under calibration, and should provide a second model thatdepends upon physical rather than electrical characteristics of thesensors.

The present invention provides such methods and systems.

DESCRIPTION OF THE PRESENT INVENTION

Rather than acquire calibration data for a TOF system by relocating atarget object over a large physical space, embodiments of the presentinvention calibrate by introducing electrical phase offset into a TOFsystem to emulate relocation of a stationary target object. As theintroduced phase shift is swept in phase, detection samples are acquiredfrom the TOF system. This process takes a relatively short time, anddoes not require mechanical repositioning of the target object, or ofthe detector sensor array relative to the target object.

The acquired data when converted to a model requires relatively smallmemory storage, perhaps 20% of the storage requirements for prior art“by example” calibration data. The acquired data is used to construct apreferably parameterized calibration phase-vs-distance model of the TOFsystem, which model requires substantially less storage space than doesthe acquired data. Once the model is constructed, the acquired data maybe discarded and the relatively compact data for the model stored. Usingcurve fitting, parameters are preferably determined that fit theacquired data to a predetermined analytical model of thedistance-vs-phase transfer function for the TOF system. During actualrun-time of the TOF system, the stored model is evaluated, rather thaninterpolated.

Model accuracy is enhanced preferably by taking into account electricaland physical characteristics of the TOF system under calibration. Morespecifically, an electrical model represents distance-vs-phasecharacteristics of the TOF system that are substantially independent ofphysical geometry. An elliptical model takes into account geometricalcharacteristics that are substantially independent of electricalcharacteristics. The elliptical model advantageously reduces so-calledelliptical error that becomes increasing important for small distancesZ, where differences in path length from TOF light source to targetobject, and TOF sensor array to target object are not negligible.

Other features and advantages of the invention will appear from thefollowing description in which the preferred embodiments have been setforth in detail, in conjunction with their accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a block diagram depicting a phase-phased, three-dimensionaltime-of-flight imaging system as exemplified by U.S. Pat. No. 6,515,740,according to the prior art;

FIGS. 1B and 1C depict exemplary waveform relationships for the blockdiagram of FIG. 1A, according to the prior art;

FIG. 1D is a block diagram depicting exemplary differentialphotodetectors and associated electronics in a fixed-phase delay (FPD)quantum efficiency modulated detector, such as may be used with thepresent invention;

FIG. 2 depicts a TOF system, calibrated and including a calibrationlook-up table, according to an embodiment of the present invention;

FIG. 3A depicts distance-vs.-phase mapping characteristics, showing thepresence of harmonic components in addition to a linear component,according to an embodiment of the present invention;

FIG. 3B depicts a TOF system during swept phase calibration mode,according to an embodiment of the present invention;

FIG. 3C is a schematic representation of phase sweeping duringcalibration mode, according to an embodiment of the present invention;

FIG. 3D depicts distance-vs-phase data acquired during the phase sweepdepicted in FIG. 3C, according to an embodiment of the presentinvention;

FIG. 3E depicts distance-vs-phase data acquired during a phase sweep,according to an embodiment of the present invention;

FIG. 3F depicts phase unwrapping of the data depicted in FIG. 3E, toavoid distance ambiguity or aliasing in modeling, according to anembodiment of the present invention;

FIG. 3G depicts translation of data point p⁰ in FIG. 3F, to the verticalaxis of FIG. 3G such that all data angles in the constructed model arepreferably referenced to 0°, according to an embodiment of the presentinvention;

FIG. 3H depicts normalization of phase data depicted in FIG. 3F,according to an embodiment of the present invention;

FIG. 3I depicts the normalized phase data of FIG. 3H converted to actualZ value, according to an embodiment of the present invention;

FIG. 4 depicts system nomenclature used to transform XY calibration datato ZUD_(ij) information, according to an embodiment of the presentinvention;

FIG. 5A depicts actual phase function data acquired for a single pixelin array 130, according to an embodiment of the present invention;

FIG. 5B depicts a parametric harmonic sine modeling term for the singlepixel whose data is shown in FIG. 5A as well as a true sinewave term,according to an embodiment of the present invention;

FIG. 5C depicts residual error resulting from the difference between thetwo waveforms shown in FIG. 5B, according to an embodiment of thepresent invention;

FIG. 6A depicts sensor geometry associated with modeling for ellipticalerror, according to an embodiment of the present invention;

FIG. 6B depicts optical path differences that give rise to ellipticalerror, according to an embodiment of the present invention;

FIG. 6C depicts elliptical error for the sensor pixel whose data isshown in FIG. 6B, according to an embodiment of the present invention;

FIGS. 7A-7E depict improvement in far edge elliptical error forincreasing distance Z for the sensor pixel whose data is shown in FIG.6B, according to an embodiment of the present invention;

FIG. 8A depicts data points from the electrical model and from actualmeasured phase at common distances Z^(n) and Z^(f) used for ellipticalerror determination, according to an embodiment of the presentinvention;

FIG. 8B depicts an elliptical error model determined from the differenceof the two curves depicted in FIG. 8A, according to an embodiment of thepresent invention;

FIG. 9A depicts phase vs. distance data and the electrical modelaccording to an embodiment of the present invention;

FIG. 9B depicts the phase error obtained by taking the differencebetween the two curves depicted in FIG. 9A, according to an embodimentof the present invention;

FIG. 9C depicts the phase data from 9B and an elliptical model obtainedusing curve fitting for the data shown in FIG. 9B, according to anembodiment of the present invention;

FIG. 10 depicts a calibration configuration using differently sizedtarget objects, according to an embodiment of the present invention; and

FIG. 11 depicts use of parallelization and/or pipelining to maximizecalibration throughput, according to an embodiment of the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

In brief, prior art “by example” calibration techniques requirerepositioning a target object relative to a TOF system and recordingdata. During run-time of the TOF system, the recorded data isinterpolated to provide calibration between phase and distance. Bycontrast, the present invention calibrates using a stationary targetobject and electrically introduces phase shift into the TOF system toemulate relocation of the target object. The relatively few data samplesthus taken are used to build a model that preferably is a parameterizedmathematical representation of the general form x+sin(x). Thephase-vs-distance model data is stored as a look-up table that isevaluated (rather than interpolated) during actual run-time operation ofthe TOF system. The acquired data may be purged once the model data hasbeen stored. Advantageously calibration according to the presentinvention takes less time to perform, perhaps minutes contrasted withtens of minutes using prior art “by example” calibration. Further,calibration according to the present invention requires less physicalspace since there is no need to repeatedly reposition the target object.In addition, the resultant model data is quite compact, typicallyrequiring a few hundred KB of storage, as contrasted with several MB ofstorage for data acquired using prior art “by example” calibration.

Modeling according to the present invention preferably includes twocomponents: (1) electrical modeling of phase-vs-distance characteristicsthat depend upon electrical rather than geometric characteristics of thesensing system, and (2) elliptical modeling of phase-vs-distancecharacteristics that depend upon geometric rather than electricalcharacteristics of the sensing system.

FIG. 2 depicts a TOF system 200 whose memory 170 stores, among otherdata, a calibration look-up table 210, obtained in calibration mode,according to an embodiment of the present invention. Elements withinsystem 200 that bear reference numerals identical to those of TOF system100 (FIG. 1A) may in fact be identical elements. In some embodiments ofthe present invention, multiple light emitters 120 may be used, asindicated in phantom in FIG. 2. As described herein, data within look-uptable 210 typically require but a few hundred KB of storage, and as suchlook-up table 210 may readily be incorporated into embedded systems.During calibration mode, system 200 clock generator circuitry 280generates a calibration phase timing signal such that detector array 130believes target object 20 disposed at distance Z is located other thandistance Z. As will be described, the present invention recognizes thatintroducing an electrical phase change into system 200 is equivalent tophysically relocating the target object 20.

Referring briefly to FIG. 1D, if such detection circuitry is included inTOF system 200, during calibration mode according to the presentinvention, the DELAY elements preferably are commanded to insert a sweptphase delay over a range preferably encompassing 0° to 360°. The phasesweep can be continuous but preferably is in discrete increments,perhaps 10°. Granularity of the sweep preferably is determined byseveral factors including hardware implementing and present operatingfrequency of the TOF clock generator 280, anticipated normal Z range forTOF system 200, etc.

As will now be described, aspects of calibration according to thepresent invention capture the fundamental electronic detectioncharacteristics of system 200, as well as geometry-related detectioncharacteristics, e.g., so-called elliptical error. Fast-Z calibrationpreferably creates a phase-to-distance mapping with as few data pointsas possible, in a time-efficient and space efficient manner. To capturethe fundamental electronic detection characteristics of system 200, thephase-vs-distance mapping should ideally be linear but includeharmonics, as shown in FIG. 3A. Further, for Z distances that are small,the physical separation between the sensor detectors 140 and lightemitter(s) 120 give rise to an elliptical error that should be modeledto ensure accurate calibration.

FIG. 3A depicts the phase-vs.-distance detection relationship for a TOFsensor system such as system 100 or system 200 and demonstrates that thetransfer function has a linear component as well as sinusoidal termsthat represent harmonic content. This relationship arises from theelectrical characteristics of sensor structure 140 and circuitry 150 andindeed array 130, and from imperfections (higher order terms) of thelight waveform from emitter(s) 120. The distance-vs.-phase mapping ofFIG. 3A is an electrical modeling that is substantially independent ofthe physical configuration of the sensor array 130 and the modulatedlight source 120. As described later herein, the distance-vs-phaserepresentation of FIG. 3A may be characterized by a parametricexpression, for example, radial distance is proportional to p+k₁sin(k₂π+2πp), where p represents phase, and k₁ and k₂ are systemparameters. For example, k₁ also models individual pixel detectorresponse and behavior to reflected light from emitter(s) 120. In theabove representation for radial distance, proportionality, rather thanequality, is used to accommodate different distance units. As describedlater herein, the present invention also models the physicalcharacteristics of the sensing system that are substantially independentof electrical characteristics. This second modeling accounts forso-called elliptical error, arising from different path lengths fromemitter(s) 120 to target object 20, and from target object 20 to sensordetectors 140 in detector array 130. At relatively short distances Z,elliptical error increases in magnitude because the above-defined pathlengths can differ substantially.

As depicted in FIG. 3B during calibration mode, phase-vs-distancecalibration data are acquired according to the present invention using astationary target object 20, shown disposed a fixed distance Z^(f) fromthe TOF system 200 under calibration. As described later herein, Z^(f)preferably is the smallest distance at which the elliptical errorbecomes sufficiently small to be ignored. In practice, when system 200(or the like) is being mass produced, Z^(f) will previously have beenempirically determined for this system type. Perhaps Z^(f) will havebeen determined to be 80 cm. For each system 200 that is mass produced,target object 20 is disposed distance Z^(f) away, and data is acquiredto build an electrical model. Building and storing the electrical modeltypically takes but a minute or so, and requires perhaps a few hundredKB of memory storage for the model. By definition, phase error atdistance Z^(f) is acceptable small, as will be phase error for Z>Z^(f).But data acquired for Z<Z^(f) will contain geometric-type ellipticalerror, and thus an elliptical error model is next constructed. As willbe described with respect to FIGS. 8A and 8B, it is sufficient toacquire phase data for a few points at distances less than Z^(f),perhaps at 60 cm, and 40 cm, where for a given model of system 200,Z^(f) is about 80 cm. Using these relatively few points, ellipticalerror is modeled, as shown in FIGS. 8A and 8B. With elliptical errorcompensation, phase data for Z<Z^(f) will be acceptable data.

As shown by FIG. 3C, during calibration mode, clock unit 280 injects asweep of phase shift offsets through a full 360° into TOF system 200. Asa result, exciter 115 causes the light waveforms emitted by lightsource(s) 120 to exhibit swept phase shift. For ease of illustration andcomprehension, FIG. 1D depicts the shift-in-phase as associated withinpixels 140 in detector array 130. However the shift in phase will becommon to all pixel detectors 140. Thus it may be more economical toimplement phase shifting within the light source path, e.g., via exciter115. In any event, it is understood that the configuration of FIG. 1D isintended to be exemplary with respect to the mechanics of phaseshifting, and other configurations are possible. A number of discretesweep phase shifts is shown in FIG. 3C, while FIG. 3D depicts theresultant phase-vs-distance transfer function for an exemplary pixel 140in detector array 130, and models the electrical detectioncharacteristics that are substantially independent of physical geometry.

With reference to FIG. 3A and FIG. 3D, as phase of the emitted lightsignal from emitter(s) 120 is swept from 0° to 360°, the effect upon TOFsystem 200 is tantamount to a relocation of target object 20 through afull unambiguous detection operating range (ZUD), perhaps 3 m for a 50MHz clock generator signal, 1.5 m for a 100 MHz clock generator signal,etc.

Sweeping of the emitted light phase as indicated in FIG. 3C preferablyis implemented by clock generator block 280 fabricated on IC chip, 210,upon which much of system 200 may be fabricated, and by exciter 115,which typically is implemented off-chip. Preferably a differentconfiguration is loaded into clock-generator block 280 and thus exciter115 has a different phase each time and therefore the phase of lightfrom emitter 120 is changed. Typically block 280 includes or is drivenby a high-speed clock operating at perhaps 1 GHz clock frequency.Preferably clock-generator block 280 can produce a minimum phase shiftof approximately 10° increments, which is sufficient to sample thedistance-phase curve for a distance accuracy of about 1 cm to 2 cm. Oncethe data is taken from sensor detector array 130, the desired analyticmodel of distance-vs-phase can be generated.

As shown by FIGS. 3E and 3F, it is desired that the distance-vs-phasemodel be unambiguous for phase changes within a 360° sweep, which is tosay the Z values should be free of aliasing. So doing preferablyinvolves unwrapping the transfer function data for p>360°. In FIG. 3F,the notation P^(f) denotes phase shift at distance Z^(f), and thenotation ZUD denotes unambiguous Z distance, even when phase p>360°.This result is achieved by upshifting by Z^(f) distance data for p>360°.In FIG. 3F, the resultant transfer function is unwrapped and unambiguousfor distances Z^(f).

In FIG. 3G, the data point for p⁰ is translated from ZUD to 0 (or ZUD),on the Z vertical axis, which optional translation advantageouslyassists in data dealiasing for long range applications where the targetmay be at an interval greater than the ZUD. Preferably the electricalmodel data depicted in FIG. 3F is next normalized such thatp=(phase−P⁰)/360° and z=Z/ZUD, while still ensuring the phase does notwrap around. Thus, FIG. 3G depicts the data of FIG. 3F transformed intoFIG. 3G and thus so normalized, this transformation operation isoptional.

Understandably it is important to identify a suitable analytic model toaccurately and succinctly describe the distance-vs-phase transferfunction relationship. One method to identify such a model is to collectdata from many three-dimensional camera systems of the same kind, i.e.,camera systems having the same physical, electrical and opticalcharacteristics. By analyzing the common properties of this data, onecan construct a parameterized function that captures the fundamentalbehavior of the camera system, perhaps system 100 or 200, and also fitsthe data well.

The calibration described herein was found to be highly effective forTOF three-dimensional camera systems such as those designed by Canesta,Inc. of Sunnyvale, Calif., assignee herein. Various aspects of these TOFsystems are described in various US patents assigned to Canesta, Inc.,including U.S. Pat. No. 7,176,438 Method and System to DifferentiallyEnhance Sensor Dynamic Range Using Enhanced Common Mode Reset, U.S. Pat.No. 7,157,685 Method and System to Enhance Differential Dynamic Rangeand Signal/Noise in CMOS Range Finding Systems Using DifferentialSensors, U.S. Pat. No. 6,919,549 Method and System to DifferentiallyEnhance Sensor Dynamic Range, U.S. Pat. No. 6,906,793 Methods andDevices for Charge Management for Three-Dimensional Sensing, U.S. Pat.No. 6,587,186 CMOS-Compatible Three-Dimensional Image Sensing UsingReduced Peak Energy, U.S. Pat. No. 6,580,496 Systems for CMOS-CompatibleThree-Dimensional Image Sensing Using Quantum Efficiency Modulation, andU.S. Pat. No. 6,515,740 Methods for CMOS-Compatible Three-DimensionalImage Sensing Using Quantum Efficiency Modulation.

The calibration model successfully used for such TOF camera systems isdefined by equation (1):R=p+k ₁ sin(k ₂π+2πp)  (1)where R is the radial distance rather than the Z distance to the targetobject from the sensor array, p is the phase measured by the sensorsystem as the modulating light source from emitter 120 is swept in phasefrom 0° to 360°, and k₁ and k₂ are parameters obtained through curvefitting. Various curve fitting techniques available in the literaturemay be used to determine k₁ and k₂, for example LMS.

Thus with respect to the normalized distance-vs-phase transfer functionshown in FIG. 3H, curve fitting may begin with the representation:Z=p+m _(ij) +A _(ij) sin(s _(ij) p+2πfp)  (2)where m_(ij) is a per pixel detector (140) DC parameter, A_(ij) is asinewave amplitude per pixel detector (140) parameter, s_(ij) is asinewave phase shift per pixel detector (140) parameter, f is a globalparameter, e.g., f=4, and where it is understood that P_(0ij) is phaseat Z^(f).

Given equation (2), actual Z may be obtained by multiplying z·ZUD, asfollows, where ZUD_(ij) is a per pixel parameter representingunambiguous Z range.Z=ZUD _(ij·) [p+m _(ij) +A _(ij) sin(s _(ij) p+2πfp)]  (3)

The result of such conversion is shown in FIG. 3I, wherein normalizedphase p=(phase−P⁰)/360°, and m_(ij), A_(ij), s_(ij), ZUD_(ij) are systemparameters.

As noted, distance R calculated by equation (1) is the radial distancebetween sensors 140 in array 130 and target object 20, and not the Zdistance. While a phase change is equivalent to moving the targetobject, this is true along the viewing axis of each pixel detector 140in array 130. Stated differently, a phase change implies moving thetarget object along the radial (R) axis, and not along the Z axis. Asnoted above, since calibration should yield Z information, radialdistances R have to be converted to Z. The relationship between R and Zis depicted in FIG. 4.

As seen in FIG. 4, one can obtain the Z distance from equation (4):Z=R/√{square root over (1+(Xij ² +Yij ²)/Zij ²)}  (4)

In equation (4), X_(ij), Y_(ij), Z_(ij) are the geometric coordinates ofthe area imaged by pixel 140-(i,j) with respect to the plane of sensorarray 130 (see FIG. 2), and the optical axis. X_(ij), Y_(ij) aredetermined by a previous XY calibration performed at a known (and fixed)distance Z_(ij). It follows from equation (4) that:ZUDij=UD/√{square root over (1+(Xij ² +Yij ²)/Zij ²)}  (5)where ZUD_(ij) differs for each pixel detector 140 in array 130, and isdetermined from XY calibration.

Methods for XY calibration are known in the art. For example, one knownmethod places a flat target having a sinusoidal pattern specially madefor XY calibration at distance Z_(ij) from the sensor (typically 1 m).From the brightness images of this target, one can calculate X_(ij) andY_(ij) locations of the area imaged by each pixel of the sensor array.The X_(ij), Y_(ij), Z_(ij) information is then stored in a separatetable, e.g., within memory 210, and subsequently used at run-time toproduce X and Y locations of the target area imaged by pixel 140-(i,j).

The results of XY calibration are also used to convert R distances to Z,per equation (4). Hence the Z-distance vs. phase relationship can beexpressed analytically using the data from the phase sweep and XYcalibration, all without having to move target object 20.

Understandably, for accurate Z information, accurate XY calibration isrequired. For a Z accuracy of 1 cm, XY calibration should be well below1 cm, and preferably only a few mm. Greater accuracy is needed forpixels near the edge of sensor array 130 since their viewing angle isgreater (and hence more sensitive). The error due to inaccuracies in XYcalibration grows with distance, and preferably calibration accuracy ischecked at the far end of the operating range.

Before describing elliptical correction, it is useful to view actualdata acquired from a pixel detector in an actual sensor array 130. FIG.5A depicts measured phase-vs-distance measurements for an actual pixel140 in an array 130 comprising 132 rows and 176 columns of pixeldetectors. FIG. 5A depicts a response over a full phase sweep. Theundulatory aspect of the response is too small to be discernable in FIG.5, which is why the response appears substantially linear. FIG. 5Bdepicts the parametric harmonic model as well as a true sinewave, in anattempt to model the phase-vs-distance response of the pixel whose datais shown in FIG. 5A. More specifically, FIG. 5B depicts phase vs.residual phase after removal of the linear term, and a superimposedmodeled sinewave term. FIG. 5C depicts the residual phase, which is thedifference between the two curves plotted in FIG. 5B.

Having described electrical Z-calibration, in which no target objectrepositioning is required, elliptical correction according to thepresent invention will now be described.

In the above-described electrical calibration method, it was assumedthat no distance-dependent behavior or “irregularity” existed in thedistance-phase relationship. However, in practice, this assumption isnot justified. There will be irregularity in the distance-phase curvedue to the physical separation between light emitter(s) 120 and array130 of sensors 140. This physical separation is denoted in FIG. 6A, andresults in light rays reflected from target object 20 back to the sensorhaving a different travel time relative to the travel time of lightemitted from source(s) and striking the target 120.

At large values of Z relative to separation distance s between emittersource(s) 120 and detectors 140, the difference (e1) in travel timesbetween two light paths is relatively constant, and changes very littlewith target object 20 distance. According to the present invention, whenelectrical calibration is performed, e1 is assumed to be constant overthe entire operating range. But when target object 20 is moved closer tosystem 200, the travel-time difference can change substantially, asdepicted in FIG. 6A by e2. The magnitude of the change, an error in theotherwise-correct electrical model, is dependent on separation distances. The smaller the separation s, the smaller the change in travel time.In the ideal case, s=0 and the error would be zero.

The error due to the difference in travel times between emitted andreflected light rays is termed elliptical error, as the locations of thesensor and the light source define an ellipsoid corresponding to pointsof fixed phase delay. Beyond a certain distance from the sensor, pointsof fixed phase delay resemble more of a sphere, and the elliptical errorbecomes zero.

FIG. 6B and FIG. 6C demonstrate the effect of elliptical error whereseparation distance s=10 cm and the viewing angle of the pixel inquestion is 45°. More particularly, FIG. 6B shows the (emitted lightpath vs. reflected light path) difference as a function of Z distance.FIG. 6C depicts resultant elliptical error, which is the first curveminus its value at infinity. From FIGS. 6B and 6C it is seen that atdistance Z=30 cm, elliptical error is about 0.5 cm, and at Z=65 cm,elliptical error is about 0.1 cm. For the data shown, in practiceelliptical error is substantially negligible beyond Z=65 cm for a sensorhaving an accuracy of 1 cm.

FIGS. 7A-7E are three-dimensional plots of elliptical error for thepixel sensor whose data is shown in FIGS. 6B and 6C. FIG. 7A depicts a30 cm elliptical error at the corner regions when Z=11 cm, and a fairlynegligible elliptical error otherwise. FIGS. 7B-7E depict a continuingdecrease in magnitude of elliptical corner error as distance Zincreases. For example, FIG. 7E depicts essentially 0 cm ellipticalerror for Z=50 cm, even at the corner regions. Thus, according to thepresent invention, electrical calibration data generated per FIG. 3Bwill be taken when Z^(f)=50 cm.

FIG. 8A depicts calculation of elliptical error using two sets of datapoints: (1) the electrical model sampled (or evaluated) at distancesZ^(n) and Z^(f), and (2) actual phase measured from the pixel sensor atthe same distances Zn and Zf. As shown in FIG. 8A at small Z values, theactual Z distance deviates from that predicted by the electrical model.For example a target object placed at distance Z^(n) cause the system tooutput a phase value of p^(N), but this phase value deviates from thevalue predicted by the electrical model. Hence at close range theelectrical model must be augmented by a correction term termedelliptical model. The elliptical correction term when added to theelectrical model provides the correct phase distance relationship forsmall values of Z distance.

In FIG. 8A, the difference between the two curves shown is depicted inFIG. 8B as the elliptical error model. As shown in FIG. 8B, theelliptical model is forced to be zero at P^(f). Generally a quadraticequation can be used to model the elliptical error. The elliptical errormodel is added to the electrical model when the phase (e.g. P^(n)) isbetween P⁰ and P^(f). For phase values outside this range, the model isassumed to be zero. As noted, this model accounts for physical andgeometric characteristics of sensors associated with TOF system 200,rather than with their electrical characteristics. With respect toelliptical model calibration nomenclature associated with FIG. 8A andFIG. 8B for data associated with a pixel sensor (i,j), preferably fouradditional parameters can be defined. P^(0ij) is understood to be partof the electrical model, where P_(0ij), P^(nij), and P^(fij) are phaserange limits wherein elliptical correction is to be applied, and K^(ij)are correction curve parameters that are forced to be zero at P^(0ij).In a preferred embodiment, two correction curve parameters K_(ij) areused for a second order model.

Using actual sensor data depicted in FIGS. 8A and 8B, FIG. 9A depictsphase-vs-distance curves for a 360° phase sweep of the same electricalmodel evaluated at two distances. The uppermost trace in FIG. 9A depictsmeasured phase-vs-distance data, whereas the lowermost trace depicts theelectrical model predicted data. Phase error is the difference betweenthe two curves shown in FIG. 9A, which difference is depicted in FIG.9B. FIG. 9C depicts the resultant elliptical model obtained by curvefitting data shown in FIG. 9B. It is seen from FIG. 9C that modelperformance is very good.

A single light source 120 was used in describing many of the aboveembodiments. However in practice preferably multiple light elements 120may be used, e.g., laser, LED, VCSEL, etc. are used. When multiple lightsources are used, elliptical error may increase because of possiblephase variations between the different light elements. At far range Z,where the data for electrical calibration is taken, illumination fromemitters 120 tends to be substantially more uniform. In practice, phasevariations between individual light sources 120 are not an issue. But asZ decreases and target object 20 moves closer to system 200, targetobject illumination becomes less uniform. Some areas of target object 20receive light only from certain light elements 120. This illuminationvariation adds to the elliptical error, but this error contribution canbe modeled as part of elliptical correction, as will now be described.

It is possible to construct pure (i.e., geometry dependent) ellipticalerror analytically from the specifications of all the system 200components. But in practice, light sources 120 non-idealities make thiserror much more complex and rather difficult to predict. One couldcreate an elaborate model that takes into account all the factorsinvolved including phase variations between different light elements120, non-uniformity of the illumination pattern, relative geometry ofthe light source and sensor array 130. However, such a model is likelyto be very complex and time consuming to build as well as to evaluate.

According to an embodiment of the present invention, elliptical errorpreferably is modeled using measured data acquired at near range,Z<Z^(f). A number, e.g., K, of distances are selected for which sensorphase data is collected. How many distances to use will depend upon thesystem 200 distance accuracy requirement and the design of system 200.Such factors can include relative geometry of sensor array 130 and lightsource(s) 120, phase variations between light source(s) 120, uniformityof illumination, etc. In practice, experimental data suggest that two tofive distances are sufficient for most camera systems. FIG. 8A depictsK=2 data points acquired for Z<Z^(f).

Once the phase data (Phase_Measured) is acquired for K distances,calibration according to the present invention carries out the followingsteps:

(1) With reference to FIG. 3B, and FIGS. 9A-9C, the entire electricalmodel is constructed, and the set of K phases (Phase_Electrical)corresponding to K distances for which elliptical data is available isextracted.

(2) the phase correction function is calculated:Perr=Phase_Measured−Phase_Electrical.

(3) With reference to exemplary FIG. 3C, curve fitting is performedwhereby data points of Perr are fit to an analytical model that is afunction of phase. Constructing the analytical model of Perr preferablyis carried out by fitting the data to an exponential, polynomial orother such function. It is usually sufficient to use such a functionwith two or three parameters to adequately model the elliptical error.This analytical model can be stored in memory 210, after which datagathered to form the model can be purged from memory. Note that Perr isa correction term for the phase before electrical calibration isapplied. At this juncture, distance Z^(f) is known, e.g., the distanceat which elliptical error is sufficiently small to be ignored. Once themodel parameters are built and stored, e.g., in memory 210 in system200, Perr can be evaluated efficiently at run time of system 200.

(4) the parameters of Perr are stored in a separate section of thecalibration table, e.g., in a portion of memory 170, perhaps portion 210(see FIG. 2).

Thus, the complete fast calibration method according to the presentinvention preferably includes the following steps:

(1) Referring to FIG. 3B, a target object 20 is placed at known Z^(f)distance, perhaps about 50 cm to about 100 cm from system 200, tocollect data for electrical calibration. The exact distance Z^(f)depends on the design of camera system 200 and is selected such thatelliptical error is negligible at this distance. As noted earlier, thesame value for Z^(f) may be used to calibrate a mass production run of agiven system type, e.g., system 200. Stated different, each same systemto be calibrated will involve modeling using a target object the samedistance Z^(f) from the system.

(2) As depicted in FIG. 3B and FIG. 3C, a phase sweep is performedwherein phase of the signal from exciter 115 that drives light source120 preferably is changed from 0° to 360° in N steps. This results in Nphase points for each pixel 140 in array 130. To minimize noise effects,for each phase setting, M frames (perhaps M=20) should be acquired fromthe sensor array and then averaged.

(3) Curve fitting is performed for the electrical model, as suggested byFIG. 3D to fit the N phase points from step (1) to a predeterminedanalytic function, resulting in a set of model parameters. PreferablyR-to-Z conversion is also done in this step using the results of XYcalibration so as to obtain the Z-distance-phase curve. R-TO-Zconversion may be carried out according to equation (4).

(4) The model parameters for all pixels 140 in array 130 preferably arestored in a calibration table 280, e.g., within memory 210 in system200. These model parameters require typically 10% to 20% the storageneeded to store data acquired using prior art “by example” calibrationtechniques. These stored model parameters are used during system 200run-time evaluation as well as for elliptical error correction.

(5) Detector sensor response is acquired at K different near distances,e.g., Z<Z^(f), for example between about 0 cm and about 50 cm to modelelliptical error, e.g., as suggested by FIG. 6C, FIG. 8A, and FIG. 8B.For each such near range distance, detector sensor phase data(Phase_Measured) is acquired, preferably using M samples and averagingas above.

(6) Calculation of phase correction function:Perr=Phase_Electrical−Phase_Measured is carried out, wherePhase_Electrical represent phase points obtained from the analytic modelcalculated in step (3), above.

Perr data points are fitted to a second analytic model that is afunction of phase, and the Perr model parameters are stored in aseparate portion of calibration table 210.

The above-described procedure can be carried out in a few minutes ascontrasted with tens of minutes for prior art calibration techniques.FIG. 10 depicts an exemplary setup used for fast-Z calibration,according to the present invention. Such setup does not requireexpensive equipment and does not require a large physical space. In step(1) above, target object 20-1 may be the largest target as it will befurther away from sensor(s) 140 than target 20-4 used in step (5). InFIG. 10, distance Zo<Z^(f). As noted, the target can be at a fixeddistance Z^(f) to simplify electrical calibration setup. Data collectionfor step 2 typically requires about one to two minutes for a full phasesweep. Target object 20-4 used in step (5) may be physically smaller andcloser to sensor 140 in system 200 under calibration. Target object 20-4may be disposed in front of system 200 robotically in automated fashion,or manually. Data collection for step (5) takes but a few seconds.Indeed, from start to finish, calibration for each system 200 undergoingcalibration can be completed in five minutes or less.

For high volume manufacturing of systems 200, parallelization andpipelining techniques can help maximize calibration throughput, e.g.,the number of systems 200 to be calibrated per unit time. FIG. 11replicates in somewhat simplified form the depiction of FIG. 10.Preferably the phase sweep operation of step (2) above is performedsimultaneously for two separate systems 200, using two separatecalibration stations. Step (2) is the most time consuming step incalibration according to the present invention, and parallelization asdepicted in FIG. 11 increases calibration throughput. The twoparallel-operating calibration stations depicted in FIG. 11 feed into athird calibration station that collects data for elliptical errormodeling step (5). In this manner, the calibration process can produceone calibrated unit 200 every one to two minutes. Understandably greaterthroughput can be achieved use additional parallelization and/orpipeline stages.

An exemplary evaluation procedure that determines Z distance from phaseaccording to an embodiment of the present invention will now bedescribed. The output of a three-dimensional camera 200 is geometricaldata obtained from acquired phase information. The conversion from phaseto geometrical data preferably is done using information stored incalibration table 210, stored in memory associated with thethree-dimensional camera system. Given a system 200 detected phase p,the corresponding Z is calculated as follows:

(1) Calculate elliptical correction Perr(p) from the model of theelliptical error that is preferably stored in memory associated withsystem 200, e.g., within memory 170.

(2) Adjust phase: p=p−Perr(p)

(3) Use the memory-stored elliptical model of distance-vs-phase curve toobtain distance: Z=Evaluate_DPcurve(p).

Several methods can be used to calculate Z at system 200 run time. Onemethod is to perform evaluations of the analytic models of ellipticalerror and distance-phase curves at run-time. For such approach, modelevaluation can be sped up by storing pre-calculated tables of the basicfunctions used in these models. For example, the “sin” function of thedistance-vs-phase curve can be tabulated over a range of 360° with astep size sufficiently small to maintain error within noise limits ofsensors 140 in array 130. A more efficient implementation of the “sin”function could also be used. While such implementation would be slightlyless accurate than an exact “sin” function, it can be made sufficientlyaccurate for the purposes of producing Z values. Another approach is tocreate a standard calibration table as per the “by-example” method. Thiscan be accomplished by tabulating the models themselves over a range of360° using a small step size to limit subsequent interpolation errors.

To summarize, a fast-Z calibration procedure according to the presentinvention is a very efficient method of calibration. Such procedure doesnot require a moving target, and most of the data capture is done at onefixed distance Z^(f) that is not far from the system under calibration.As such, the physical space needed for calibration is reasonable. Fast-Zcalibration according to the present invention utilizes XY calibrationand requires an acceptable level of accuracy from such XY calibration.Embodiments of the present invention preferably capture phase data at afew distances close to the system under calibration, to model complexelliptical error. This step can be accommodated without much difficultyduring calibration setup. Analytic models of the distance-phase curveand elliptical error preferably ensure that any error involved inevaluating these models is minimized.

While embodiments of the present invention have been described withrespect to phase-based TOF type systems, the underlying approach shouldbe adaptable to systems that acquire other type of data. For example,U.S. Pat. No. 6,323,942 CMOS-Compatible Three-Dimensional Image SensorIC, assigned to Canesta, Inc., assignee herein, describes a pure TOFsystem. Z distance is determined by the round trip time for opticalenergy to be emitted by the TOF system, to reflect off a target object,and to be detected by the TOF system. Although not yet tested,calibration of the sensor array within such TOF system might beaccomplished by injected time delay into the emitted optical energy,such that more injected time delay would emulate a target object fartheraway. In the broadest sense, then, the present invention encompassesrapid calibration of a system that detects one parameter (e.g., phase,or time) to determine a desired value, e.g., distance to a targetobject. Calibration according to embodiments of the present inventioninvolves injected into such system perturbations into the detectedparameter to emulate repositioning of the target object. In constructingthe electrical model, it is understood that a sufficient number ofsamples must be acquired to adequately represent the phase-vs-distancecurve. It is also understood that phase increments need not be equal inmagnitude, e.g., some phase increments may be smaller or larger thanothers. For example if the phase-vs-distance curve changes slowly in aregion, fewer phase samples will suffice for that region.

Modifications and variations may be made to the disclosed embodimentswithout departing from the subject and spirit of the invention asdefined by the following claims.

1. A method of calibrating a time-of-flight (TOF) system of the typethat emits optical energy of a known phase, detects a portion of saidoptical energy reflected from a target object a distance Z away, anddetermines Z by examining phase shift in detected reflected opticalenergy relative to said known phase of emitted optical energy, themethod comprising the following steps: (a) disposing a target object adistance Z^(x) from said TOF system, said distance Z^(x) being withinoperating distance range of said TOF system; (b) altering said knownphase of said emitted optical energy by at least two known phase values;(c) for each known phase value of said emitted optical energy,determining from detected reflected optical energy a corresponding phaseshift relative to said known phase; (d) using corresponding relativephase shift determined at step (c) to form an electrical model ofdetection characteristics of said TOF system; (e) storing datarepresenting said electrical model; wherein data stored at step (e) isuseable during run-time operation of said TOF system to providecalibrated values of Z responsive to phase shift in detected reflectedoptical energy.
 2. The method of claim 1, where said Z^(x) is a shortestdistance Z^(f) whereat elliptical error arising from geometry of phasedetection of said TOF system is negligible.
 3. The method of claim 1,wherein step (b) includes sweeping said first phase with incrementalvalues of phase having at least one characteristic selected from a groupconsisting of (i) increments between each of said phase values are equalin magnitude, (ii) increments between at least some of said phase valueshave different magnitude, and (iii) sweeping encompasses substantially arange of about 0° to about 360°.
 4. The method of claim 1, wherein step(e) includes storing said data representing said electrical model withinsaid TOF system.
 5. The method of claim 1, wherein step (d) includesforming said electrical model as a parametric function characterized byat least two parameters.
 6. The method of claim 1, wherein step (b)includes sweeping said known phase with incremental values of phaseexceeding 360°, and wherein step (d) includes unwrapping relative phaseshift determined at step (c) to avoid distance ambiguity.
 7. The methodof claim 1, wherein said model formed at step (d) includes a linearfactor and a sinusoid factor.
 8. The method of claim 1, wherein: saidTOF system includes an array of detectors; said model formed at step (d)approximates Z =ZUD_(ij)·[p+m_(ij)+A_(ij)sin(s_(ij)p+2πfp)], where atleast two parameters of ZUD_(ij), m_(ij), A_(ij), and s_(ij) are perdetector parameters, f is a global TOF system parameter, and p is phase.9. The method of claim 1, further including a step of dealiasing phaseshift in said detected reflected optical energy, whereby said electricalmodel formed at step (d) is useable during run-time operation of saidTOF system for unwrapped phase exceeding 360°.
 10. The method of claim1, wherein step (d) further includes forming an elliptical error modelto correct phase-vs-distance data for geometric characteristics of saidTOF system.
 11. The method of claim 10, wherein said elliptical modelformed at step (d) is useable when Z<Z^(f), where Z^(f) is a shortestdistance at which elliptical error for said TOF system is negligible.12. The method of claim 10, wherein forming an elliptical error modelincludes the following steps: (i) disposing a target object at at leastone distance Z^(y)Z<^(f) from said TOF system, where Z^(f) is a shortestdistance whereat elliptical error arising from geometry of phasedetection of said TOF system is negligible; (ii) for each said distanceZ^(y), determining from detected reflected optical energy acorresponding phase shift relative to said known phase; (iii) for eachsaid distance Z^(y), obtaining a phase value from said electrical modelformed at step (d); (iv) obtaining a difference in phase value betweenphase determined at step (ii) and phase obtained from step (iii), andusing said difference in phase to form an elliptical error model;wherein said elliptical error model is useable during run-time operationof said TOF system to provide improved calibrated values of Z<Z^(f)responsive to phase shift in detected reflected optical energy.
 13. Themethod of claim 12, wherein step (iv) includes forming said ellipticalerror model as a parametric function.
 14. A method of improvingelliptical error calibration in a time-of-flight (TOF) system of thetype that emits optical energy of a known phase, detects a portion ofsaid optical energy reflected from a target object a distance Z away,and determines Z by examining phase shift in detected reflected opticalenergy relative to said known phase of emitted optical energy, themethod comprising the following steps: (i) disposing a target object atat least one distance Z^(y)<Z^(f) from said TOF system, where Z^(f) is ashortest distance whereat elliptical error arising from geometry ofphase detection of said TOF system is negligible; (ii) for each saiddistance Z^(y) determining from detected, reflected optical energy acorresponding phase shift relative to said known phase; (iii) for eachsaid distance Z^(y), obtaining a phase value from an electrical model ofphase-vs-distance formed for said TOF system; (iv) obtaining adifference in phase value between phase determined at step (ii) andphase obtained from step (iii), and using said difference in phase toform an elliptical error model; wherein said elliptical error model isuseable during run-time operation of said TOF system to provide improvedcalibrated values of Z<Z^(f) responsive to phase shift in detectedreflected optical energy.
 15. The method of claim 14, wherein step (iv)includes forming said elliptical error model as a parametric function.16. The method of claim 14, wherein step (iv) includes storing saidelliptical error model in memory useable by said TOF system duringrun-time operation of said TOF system.
 17. A time-of-flight (TOF) systemof the type that emits optical energy of a known phase, detects aportion of said optical energy reflected from a target object a distanceZ away, and determines Z by examining phase shift in detected reflectedoptical energy relative to said known phase of emitted optical energy,the TOF including means for altering known phase emitted by said TOEsystem, and further including memory storing a distance-vs-phasecalibration model used to calibrate said TOF system, said calibrationmodel obtained according to a method comprising the following steps: (a)disposing a target object a distance Z^(x) from said TOF system, saiddistance Z^(x) being within operating distance range of said TOF system;(b) causing said means for altering known phase to vary said known phaseof said emitted optical energy by at least two known phase values; (c)for each known phase value of said emitted optical energy, determiningfrom detected reflected optical energy a corresponding phase shiftrelative to said known phase; (d) using corresponding relative phaseshift determined at step (c) to form an electrical model of detectioncharacteristics of said TOE system; (e) storing data representing saidelectrical model in said memory; wherein data stored in memory at step(e) is useable during run-time operation of said TOF system to providecalibrated values of Z responsive to phase shift in detected reflectedoptical energy.
 18. The TOF system of claim 17, wherein at step (a),said Z^(x) is a shortest distance Z^(f) whereat elliptical error arisingfrom geometry of phase detection of said TOF system is negligible. 19.The TOF system of claim 17, wherein said memory further includes anelliptical model of detection characteristics of said TOF system thatare substantially independent of electrical characteristics, saidelliptical model being used at distances Z<Z^(f), where Z^(f) is ashortest distance at which elliptical error is substantially negligible.20. The TOF system of claim 19, wherein said elliptical model ofdetection characteristics stored in said memory is formed as follows:(i) disposing a target object at at least one distance Z^(y)<Z^(f) fromsaid TOF system, where Z^(f) is a shortest distance whereat ellipticalerror arising from geometry of phase detection of said TOE system isnegligible; (ii) for each said distance Z^(y), determine from detectedreflected optical energy a corresponding phase shift relative to saidknown phase; (iii) for each said distance Z^(y), obtain a phase valuefrom said electrical model formed at step (d); (iv) obtain a differencein phase value between phase determined at step (ii) and phase obtainedfrom step (iii), and use said difference in phase to form an ellipticalerror model; wherein said elliptical error model is useable duringrun-time operation of said TOF system to provide improved calibratedvalues of Z<Z^(f) responsive to phase shift in detected reflectedoptical energy.